This chapter shows how to describe data that arrives in class intervals: how to read the table, estimate the mean, draw an ogive and compare spread using quartiles. It belongs to SPM Mathematics and sits in the Form 5 route.
How do the lessons connect?
One frequency table feeds every calculation. The order below follows the way a table is built and then used.
- Reading class intervals and cumulative frequency: boundaries, class size, midpoints and the cumulative column.
- Estimating mean from grouped data: midpoints multiplied by frequencies.
- Constructing and interpreting an ogive: plotting the cumulative column and reading the median and quartiles.
- Comparing grouped data using quartiles and spread: deciding which set is more consistent.
One table, three answers
A class of 20 students sits a quiz, and the marks are grouped as 1 to 5 (4 students), 6 to 10 (10 students) and 11 to 15 (6 students). The modal class is 6 to 10, because it has the highest frequency.
The midpoints are 3, 8 and 13. The estimated mean is (4 × 3 + 10 × 8 + 6 × 13) ÷ 20 = 170 ÷ 20 = 8.5. The cumulative frequencies are 4, 14 and 20, so the median sits in the class 6 to 10, because the 10th student falls there.
Each lesson takes one of those steps and slows it down.
Who should start where?
A student new to the chapter should read the lessons in order and finish with the practice set. A student who can build tables but loses marks on graphs can go straight to the ogive lesson.
If range, quartiles and standard deviation for single values feel new, revise dispersion of ungrouped data first. Use the descriptive statistics explorer to check your answers on invented data. For a teacher to watch a table being built, see online one-to-one Mathematics tuition.